Tuesday, June 23, 2015

What are x and y if (x-1)/i + (y+1)/2 = (x+2)/3 + (y-1)/i ?

What are x and y if (x-1)/i + (y+1)/2 = (x+2)/3 +
(y-1)/i


(x-1)/i +(y+1)/2 = (x+2)/3 +(y-i)/i. We bring both
sides to x+yi form.


(y+1)/2+(x-1)i/i^2  = (x+2)/3
+(y-1)i)/i^2.


(y+1)/2 - (x-1)i = (x+2)/3 - (y-1)i , as i^2
= 1.


We equate real parts on both sides and then equate
imaginary parts on both sides:


Real parts: (y+1)/2 =
(x+2)/3


=>3(y+1) =
2(x+2).


=> 3y-2x =
1....(1).


Imaginary parts: x-1 =
y-1.


=> x=
y.....(2).


So putting x= y in (1), we get: 3x-22x = 1. So
x= 1.


Therefore x= 1 . From (2),  y = x=
1.


So x= 1 and y = 1.

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